Method for measuring fracture toughness of glass

ABSTRACT

Glass-based articles are provided that exhibit improved drop performance. The relationship between properties attributable to the glass composition and stress profile of the glass-based articles are provided that indicate improved drop performance.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.16/425,217 filed May 29, 2019, which claims priority to U.S. ApplicationNo. 62/678,560 filed May 31, 2018, both of which are incorporated byreference herein in their entirety.

BACKGROUND Field

The present specification generally relates to glass compositionssuitable for use as cover glass for electronic devices.

Technical Background

The mobile nature of portable devices, such as smart phones, tablets,portable media players, personal computers, and cameras, makes thesedevices particularly vulnerable to accidental dropping on hard surfaces,such as the ground. These devices typically incorporate cover glasses,which may become damaged upon impact with hard surfaces. In many ofthese devices, the cover glasses function as display covers, and mayincorporate touch functionality, such that use of the devices isnegatively impacted when the cover glasses are damaged.

There are two major failure modes of cover glass when the associatedportable device is dropped on a hard surface. One of the modes isflexure failure, which is caused by bending of the glass when the deviceis subjected to dynamic load from impact with the hard surface. Theother mode is sharp contact failure, which is caused by introduction ofdamage to the glass surface. Impact of the glass with rough hardsurfaces, such as asphalt, granite, etc., can result in sharpindentations in the glass surface. These indentations become failuresites in the glass surface from which cracks may develop and propagate.

Glass can be made more resistant to flexure failure by the ion-exchangetechnique, which involves inducing compressive stress in the glasssurface. However, the ion-exchanged glass will still be vulnerable todynamic sharp contact, owing to the high stress concentration caused bylocal indentations in the glass from the sharp contact.

It has been a continuous effort for glass makers and handheld devicemanufacturers to improve the resistance of handheld devices to sharpcontact failure. Solutions range from coatings on the cover glass tobezels that prevent the cover glass from impacting the hard surfacedirectly when the device drops on the hard surface. However, due to theconstraints of aesthetic and functional requirements, it is verydifficult to completely prevent the cover glass from impacting the hardsurface.

It is also desirable that portable devices be as thin as possible.Accordingly, in addition to strength, it is also desired that glasses tobe used as cover glass in portable devices be made as thin as possible.Thus, in addition to increasing the strength of the cover glass, it isalso desirable for the glass to have mechanical characteristics thatallow it to be formed by processes that are capable of making thin glassarticles, such as thin glass sheets.

Accordingly, a need exists for glasses that can be strengthened, such asby ion exchange, and that have the mechanical properties that allow themto be formed as thin glass articles.

SUMMARY

According to aspect (1), a glass-based article is provided. Theglass-based article comprises: a compressive stress layer extending froma surface of the glass-based article to a depth of compression. Theglass-based article is characterized by K_(IC) ²×DOC/t×√{square rootover (STE)}≥7.0×10¹¹ Pa^(2.5) m^(1.5) where K_(IC) is the fracturetoughness in Pa·m^(0.5) of a glass-based substrate having a compositionand phase assemblage equivalent to the composition and phase assemblageat the center of the glass-based article, DOC is the depth ofcompression in meters, t is the thickness of the glass-based article inmeters, and STE is the stored strain energy of the glass-based articlein Pa·m.

According to aspect (2), the glass-based article of aspect (1) isprovided, wherein: K_(IC) ²×DOC/t×√{square root over (STE)}≥8.0×10¹¹Pa^(2.5) m^(1.5).

According to aspect (3), the glass-based article of aspect (1) or (2) isprovided, wherein: K_(IC) ²×DOC/t×√{square root over (STE)}≥9.0×10¹¹Pa^(2.5) m^(1.5).

According to aspect (4), the glass-based article of any of aspects (1)to (3) is provided, wherein: K_(IC) ²×DOC/t×√{square root over(STE)}≥9.5×10 ¹¹ Pa^(2.5) m^(1.5).

According to aspect (5), the glass-based article of any of aspects (1)to (4) is provided, wherein: K₁₂×DOC/t×√{square root over(STE)}≥1.0×10¹² Pa^(2.5) m^(1.5).

According to aspect (6), a glass-based article is provided. Theglass-based article comprises: a compressive stress layer extending froma surface of the glass-based article to a depth of compression. Theglass-based article is characterized by K_(IC) ²×DOC×√{square root over(STE)}≥5.6×10⁸ Pa^(2.5) m^(2.5) where K_(IC) is the fracture toughnessin Pa·m^(0.5) of a glass-based substrate having a composition and phaseassemblage equivalent to the composition and phase assemblage at thecenter of the glass-based article, DOC is the depth of compression inmeters, t is the thickness of the glass-based article in meters, and STEis the stored strain energy of the glass-based article in Pa·m.

According to aspect (7), the glass-based article of aspect (6) isprovided, wherein: K_(IC) ²×DOC×√{square root over (STE)}≥6.0×10⁸Pa^(2.5) m^(2.5).

According to aspect (8), the glass-based article of aspect (6) or (7) isprovided, K_(IC) ²×DOC×√{square root over (STE)}≥7.0×10⁸ Pa^(2.5)m^(2.5).

According to aspect (9), the glass-based article of any of aspects (6)to (8) is provided, wherein: K_(IC) ²×DOC×√{square root over(STE)}≥8.0×10⁸ Pa^(2.5) m^(2.5).

According to aspect (10), a glass-based article is provided. Theglass-based article comprises: a compressive stress layer extending froma surface of the glass-based article to a depth of compression. Theglass-based article is characterized by K_(IC) ²×DOC×H/E×√{square rootover (STE)}≥4.1×10⁷ Pa^(2.5) m^(2.5) where K_(IC) is the fracturetoughness in Pa·m^(0.5) of a glass-based substrate having a compositionand phase assemblage equivalent to the composition and phase assemblageat the center of the glass-based article, DOC is the depth ofcompression in meters, H is the hardness in Pascals of a glass-basedsubstrate having a composition and phase assemblage equivalent to thecomposition and phase assemblage at the center of the glass-basedarticle, E is the Young's modulus in Pascals of a glass-based substratehaving a composition and phase assemblage equivalent to the compositionand phase assemblage at the center of the glass-based article, and STEis the stored strain energy of the glass-based article in Pa·m.

According to aspect (11), the glass-based article of aspect (10) isprovided, wherein: K_(IC) ²×DOC×√{square root over (STE)}≥4.5×10⁷Pa^(2.5) m^(2.5).

According to aspect (12), the glass-based article of aspect (10) or (11)is provided, wherein: K_(IC) ²×DOC×√{square root over (STE)}≥5.0×10⁷Pa^(2.5) m^(2.5).

According to aspect (13), the glass-based article of any of aspects (10)to (12) is provided, wherein: K_(IC) ²×DOC×√{square root over(STE)}≥5.5×10⁷ Pa^(2.5) m^(2.5).

According to aspect (14), the glass-based article of any of thepreceding aspects is provided, wherein DOC≥75 μm.

According to aspect (15), the glass-based article of any of thepreceding aspects is provided, wherein DOC≤300 μm.

According to aspect (16), the glass-based article of any of thepreceding aspects is provided, wherein DOC≤0.4t.

According to aspect (17), the glass-based article of any of thepreceding aspects is provided, wherein DOC≥0.1t.

According to aspect (18), the glass-based article of any of thepreceding aspects is provided, comprising a maximum central tension CTgreater than or equal to 95 MPa.

According to aspect (19), the glass-based article of any of thepreceding aspects is provided, comprising a maximum central tension CTless than or equal to 120/√{square root over (t)} MPa, where t is in mm.

According to aspect (20), the glass-based article of any of thepreceding aspects is provided, wherein the glass-based article has athickness t≤1.0 mm.

According to aspect (21), the glass-based article of any of thepreceding aspects is provided, wherein the glass-based article has athickness t≥0.3 mm.

According to aspect (22), the glass-based article of any of thepreceding aspects is provided, wherein STE≥20 Pa·m.

According to aspect (23), the glass-based article of any of aspects (1)to (21) is provided, wherein 5 Pa·m≤STE≤10 Pa·m.

According to aspect (24), the glass-based article of any of thepreceding aspects is provided, wherein the compressive stress layercomprises a compressive stress CS of greater than or equal to 100 MPa.

According to aspect (25), the glass-based article of any of thepreceding aspects is provided, wherein the compressive stress layercomprises a compressive stress CS of greater than or equal to 400 MPa.

According to aspect (26), the glass-based article of any of thepreceding aspects is provided, wherein the compressive stress layercomprises a compressive stress CS of less than or equal to 1300 MPa.

According to aspect (27), the glass-based article of any of thepreceding aspects is provided, wherein the glass-based article comprisesa glass ceramic.

According to aspect (28), the glass-based article of any of thepreceding aspects is provided, wherein the glass-based article comprisesSiO₂, Al₂O₃, B₂O₃, and at least one alkali metal oxide.

According to aspect (29), the glass-based article of any of thepreceding aspects is provided, wherein a glass-based substrate having acomposition and phase assemblage equivalent to the composition and phaseassemblage at the center of the glass-based article has a K_(IC) greaterthan or equal to 0.75 MPa√{square root over (m)}.

According to aspect (30), the glass-based article of any of thepreceding aspects is provided, wherein a glass-based substrate having acomposition and phase assemblage equivalent to the composition and phaseassemblage at the center of the glass-based article has a K_(IC) lessthan or equal to 1.5 MPa√{square root over (m)}.

According to aspect (31), the glass-based article of any of thepreceding aspects is provided, wherein a glass-based substrate having acomposition and phase assemblage equivalent to the composition and phaseassemblage at the center of the glass-based article has a hardness Hgreater than or equal to 6.0 GPa.

According to aspect (32), the glass-based article of any of thepreceding aspects is provided, wherein a glass-based substrate having acomposition and phase assemblage equivalent to the composition and phaseassemblage at the center of the glass-based article has a hardness Hless than or equal to 8.0 GPa.

According to aspect (33), the glass-based article of any of thepreceding aspects is provided, wherein a glass-based substrate having acomposition and phase assemblage equivalent to the composition and phaseassemblage at the center of the glass-based article has a Young'smodulus E greater than or equal to 80 GPa.

According to aspect (34), the glass-based article of any of thepreceding aspects is provided, wherein a glass-based substrate having acomposition and phase assemblage equivalent to the composition and phaseassemblage at the center of the glass-based article has a Young'smodulus E less than or equal to 120 GPa.

According to aspect (35), a method is provided. The method comprises:ion exchanging a glass-based substrate to form a glass-based articlehaving a compressive stress layer extending from a surface of theglass-based article to a depth of compression. The glass-based articleis characterized by K_(IC) ²×DOC/t×√{square root over (STE)}≥7.0×10⁷Pa^(2.5) m^(2.5) where K_(IC) is the fracture toughness in Pa·m^(0.5) ofthe glass-based substrate, DOC is the depth of compression in meters, tis the thickness of the glass-based article in meters, and STE is thestored strain energy of the glass-based article in Pa·m.

According to aspect (36), a method is provided. The method comprises:ion exchanging a glass-based substrate to form a glass-based articlehaving a compressive stress layer extending from a surface of theglass-based article to a depth of compression. The glass-based articleis characterized by K_(IC) ²×DOC/t×√{square root over (STE)}≥4.1×10⁷Pa^(2.5) m^(2.5) where K_(IC) is the fracture toughness in Pa·m^(0.5) ofthe glass-based substrate, DOC is the depth of compression in meters, His the hardness in Pascals of the glass-based substrate, E is theYoung's modulus in Pascals of the glass-based substrate, and STE is thestored strain energy of the glass-based article in Pa·m.

According to aspect (37), the method of aspect (35) or (36) is provided,wherein the glass-based substrate comprises a glass ceramic.

According to aspect (38), the method of any of aspects (35) to (37) isprovided, wherein the ion exchanging comprises contacting theglass-based substrate with a molten salt bath.

According to aspect (39), the method of aspect (38) is provided, whereinthe molten salt bath comprises at least one of sodium nitrate andpotassium nitrate.

According to aspect (40), the method of aspect (38) or (39) is provided,wherein the contacting extends for greater than or equal to 4 hours toless than or equal to 48 hours.

According to aspect (41), the method of any of aspects (38) to (40) isprovided, wherein during the contacting the molten salt bath is at atemperature of greater than or equal to 400° C. to less than or equal to500° C.

According to aspect (42), a glass-based article produced by the methodof any of aspects (35) to (41).

According to aspect (43), a consumer electronic product is provided. Theconsumer electronic product comprises: a housing having a front surface,a back surface and side surfaces; electrical components provided atleast partially within the housing, the electrical components includingat least a controller, a memory, and a display, the display beingprovided at or adjacent the front surface of the housing; and a coverglass disposed over the display, wherein at least one of a portion ofthe housing or a portion of the cover glass comprises the glass-basedarticle of any of aspects (1) to (34) or (42).

Additional features and advantages will be set forth in the detaileddescription which follows, and in part will be readily apparent to thoseskilled in the art from that description or recognized by practicing theembodiments described herein, including the detailed description whichfollows, the claims, as well as the appended drawings.

It is to be understood that both the foregoing general description andthe following detailed description describe various embodiments and areintended to provide an overview or framework for understanding thenature and character of the claimed subject matter. The accompanyingdrawings are included to provide a further understanding of the variousembodiments, and are incorporated into and constitute a part of thisspecification. The drawings illustrate the various embodiments describedherein, and together with the description serve to explain theprinciples and operations of the claimed subject matter.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic representation of a sample utilized to determinethe fracture toughness K_(IC) and a cross-section thereof,

FIG. 2 schematically depicts a cross section of a glass-based articlehaving compressive stress layers on surfaces thereof according toembodiments disclosed and described herein;

FIG. 3A is a plan view of an exemplary electronic device incorporatingany of the glass-based articles disclosed herein;

FIG. 3B is a perspective view of the exemplary electronic device of FIG.3A;

FIG. 4 is a plot of drop performance as a function of formula (I) valuesfor various comparative examples and embodiments; and

FIG. 5 is a plot of drop performance as a function of formula (II)values for various comparative examples and embodiments.

DETAILED DESCRIPTION

Reference will now be made in detail to glass-based articles accordingto various embodiments. As utilized herein, “glass-based” indicates anarticle that includes a glass, such as glass or glass-ceramiccompositions. In general, a “glass-based substrate” refers to an articleprior to ion exchange, and a “glass-based article” refers to an ionexchanged article.

The glass-based articles exhibit improved drop performance. Theglass-based articles include a compressive stress layer extending from asurface of the glass-based article to a depth of compression. Theglass-based articles exhibit a minimum value of formulas that correlateto the desired drop performance based on a variety of propertiesinfluenced by the glass composition and the stress profilecharacteristics of the glass-based articles.

In some embodiments, the glass-based articles are characterized by thefollowing formula (I):

${K_{IC}^{2}\frac{DOC}{t}\sqrt{STE}} \geq {{7.0} \times 10^{11}{Pa}^{2.5}m^{1.5}}$

where K_(IC) is the fracture toughness in Pa·m^(0.5) of a glass-basedsubstrate having a composition and phase assemblage equivalent to thecomposition and phase assemblage at the center of the glass-basedarticle, DOC is the depth of compression in meters, t is the thicknessof the glass-based article in meters, and STE is the stored tensileenergy of the glass-based article in Pa·m. The dependence of formula (I)on the thickness of the glass-based article allows the comparison of theperformance of glass-based articles across different thicknesses. Inembodiments, the glass-based articles may exhibit values of formula (I)greater than or equal to 8.0×10¹¹ Pa^(2.5) m^(1.5), such as greater thanor equal to greater than or equal to 9.0×10¹¹ Pa^(2.5) m^(1.5), greaterthan or equal to 9.5×10¹¹ Pa^(2.5) m^(1.5), greater than or equal to1.0×10¹² Pa^(2.5) m^(1.5), or more.

In some embodiments, the glass-based articles are characterized by thefollowing formula (IA):

K _(IC) ² DOC√{square root over (STE)}≥5.6×10⁸ Pa^(2.5) m^(2.5)

where K_(IC) is the fracture toughness in Pa·m^(0.5) of a glass-basedsubstrate having a composition and phase assemblage equivalent to thecomposition and phase assemblage at the center of the glass-basedarticle, DOC is the depth of compression in meters, and STE is thestored tensile energy of the glass-based article in Pa·m. Inembodiments, the glass-based articles may exhibit values of formula (IA)greater than or equal to 6.0×10⁸ Pa^(2.5) m^(2.5), such as greater thanor equal to greater than or equal to 6.5×10 Pa^(2.5) m^(2.5), greaterthan or equal to 7.5×10⁸ Pa^(2.5) m^(2.5), greater than or equal 8.0×10⁸Pa^(2.5) m^(2.5), or more.

In some embodiments, the glass-based articles are characterized by thefollowing formula (II):

${K_{IC}^{2}{DOC}\frac{H}{E}\sqrt{STE}} \geq {{4.1} \times 10^{7}{Pa}^{2.5}m^{2.5}}$

where K_(IC) is the fracture toughness in Pa·m^(0.5) of a glass-basedsubstrate having a composition and phase assemblage equivalent to thecomposition and phase assemblage at the center of the glass-basedarticle, DOC is the depth of compression in meters, H is the hardness inPascals of a glass-based substrate having a composition and phaseassemblage equivalent to the composition and phase assemblage at thecenter of the glass-based article, E is the Young's modulus in Pascalsof a glass-based substrate having a composition and phase assemblageequivalent to the composition and phase assemblage at the center of theglass-based article, and STE is the stored tensile strain energy of theglass-based article in Pa·m. In embodiments, the glass-based articlesmay exhibit values of formula (II) greater than or equal to 4.5×10⁷Pa^(2.5) m^(2.5), such as greater than or equal to 5.0×10⁷ Pa^(2.5)m^(2.5), greater than or equal to 5.5×10⁷ Pa^(2.5) m^(2.5), or more.

The glass-based articles that satisfy either or both of formulas (I),(IA), and (II) exhibit improved drop performance, a quality that makesthe glass-based articles particularly suitable for use in electronicdevices. In this manner, the effect of the particular combination ofproperties attributable to the glass composition and the propertiesattributable to the stress profile of the glass-based articles may beconsidered as a whole when selecting glass-based articles for use inelectronic devices. The K_(IC) is included in the formulas as indicatingthe energy necessary to propagate a crack, and failure of theglass-based articles is dependent at least in part on the propagation ofa crack into the tensile region. The drop performance is proportional tothe square of the K_(IC). The DOC is included in the formulas asindicating the depth to which a crack must propagate to reach thetensile region, with deeper a DOC providing greater resistance tofailure by requiring a greater crack propagation depth before reachingthe tensile region. The STE is included in the formulas as indicative ofthe degree of strengthening due to ion exchange, which may increase theresistance to failure of the glass-based article. The square root of theSTE is incorporated due to the relationship between the square root ofthe STE and the frangibility limit of the glass-based article.

In formulas (I), (IA), and (II), the properties that refer to aglass-based substrate having a composition and phase assemblageequivalent to the composition and phase assemblage at the center of theglass-based article generally are dependent on the composition and phaseassemblage of the glass-based substrate that was ion exchanged to formthe glass-based article. In practice, the composition and phaseassemblage at the center of the glass-based article may be measured bytechniques known in the art, and the K_(IC), H, and E values ofglass-based substrates produced having the measured composition andphase assemblage may be measured. Additionally, the center of theglass-based article is not affected by or minimally affected by the ionexchange process, such that the composition and phase assemblage at thecenter of the glass-based article is substantially the same or the sameas the composition of the glass-based substrate. For this reason, theK_(IC), H, and E values of a glass-based substrate having thecomposition and phase assemblage at the center of the glass-basedarticle may be determined by measuring these properties of theglass-based substrate before the ion exchange treatment.

The properties of the glass-based articles will now be discussed. Theseproperties can be achieved by modifying the component amounts of theglass-based composition or the stress profile of the glass-basedarticle.

Compositions utilized to form the glass-based articles according toembodiments have a high fracture toughness (K_(IC)). As demonstrated byformulas (I) and (II) above, the fracture toughness has a stronginfluence on the drop performance of the glass-based articles.

In some embodiments, the compositions utilized to form the glass-basedarticles exhibit a K_(IC) value greater than or equal to 0.75MPa·m^(0.5), such as greater than or equal to 0.76 MPa·m^(0.5), greaterthan or equal to 0.77 MPa·m^(0.5), greater than or equal to 0.78MPa·m^(0.5), greater than or equal to 0.79 MPa·m^(0.5), greater than orequal to 0.80 MPa·m^(0.5), greater than or equal to 0.81 MPa·m^(0.5),greater than or equal to 0.82 MPa·m^(0.5), greater than or equal to 0.83MPa·m^(0.5), greater than or equal to 0.84 MPa·m^(0.5), greater than orequal to 0.86 MPa·m^(0.5), greater than or equal to 0.87 MPa·m^(0.5),greater than or equal to 0.88 MPa·m^(0.5), greater than or equal to 0.89MPa·m^(0.5), greater than or equal to 0.90 MPa·m^(0.5), greater than orequal to 0.91 MPa·m^(0.5), greater than or equal to 0.92 MPa·m^(0.5),greater than or equal to 0.93 MPa·m^(0.5), greater than or equal to 0.94MPa·m^(0.5), greater than or equal to 0.95 MPa·m^(0.5), greater than orequal to 0.96 MPa·m^(0.5), greater than or equal to 0.97 MPa·m^(0.5),greater than or equal to 0.98 MPa·m^(0.5), greater than or equal to 0.99MPa·m^(0.5), greater than or equal to 1.00 MPa·m^(0.5), greater than orequal to 1.01 MPa·m^(0.5), greater than or equal to 1.02 MPa·m^(0.5),greater than or equal to 1.03 MPa·m^(0.5), greater than or equal to 1.04MPa·m^(0.5), greater than or equal to 1.05 MPa·m^(0.5), greater than orequal to 1.06 MPa·m^(0.5), greater than or equal to 1.07 MPa·m^(0.5),greater than or equal to 1.08 MPa·m^(0.5), greater than or equal to 1.09MPa·m^(0.5), greater than or equal to 1.10 MPa·m^(0.5), greater than orequal to 1.11 MPa·m^(0.5), greater than or equal to 1.12 MPa·m^(0.5),greater than or equal to 1.13 MPa·m^(0.5), greater than or equal to 1.14MPa·m^(0.5), greater than or equal to 1.15 MPa·m^(0.5), greater than orequal to 1.16 MPa·m^(0.5), greater than or equal to 1.17 MPa·m^(0.5),greater than or equal to 1.18 MPa·m^(0.5), greater than or equal to 1.19MPa·m^(0.5), greater than or equal to 1.20 MPa·m^(0.5), greater than orequal to 1.21 MPa·m^(0.5), greater than or equal to 1.22 MPa·m^(0.5),greater than or equal to 1.23 MPa·m^(0.5), greater than or equal to 1.24MPa·m^(0.5), greater than or equal to 1.25 MPa·m^(0.5), greater than orequal to 1.26 MPa·m^(0.5), greater than or equal to 1.27 MPa·m^(0.5),greater than or equal to 1.28 MPa·m^(0.5), greater than or equal to 1.29MPa·m^(0.5), greater than or equal to 1.30 MPa·m^(0.5), greater than orequal to 1.31 MPa·m^(0.5), greater than or equal to 1.32 MPa·m^(0.5),greater than or equal to 1.33 MPa·m^(0.5), or greater than or equal to1.34 MPa·m^(0.5). In embodiments, the compositions utilized to form theglass-based articles exhibit a K_(IC) value greater than or equal to0.75 MPa·m^(0.5) to less than or equal to 1.34 MPa·m^(0.5), such as fromgreater than or equal to 0.76 MPa·m^(0.5) to less than or equal to 1.33MPa·m^(0.5), from greater than or equal to 0.77 MPa·m^(0.5) to less thanor equal to 1.32 MPa·m^(0.5), from greater than or equal to 0.78MPa·m^(0.5) to less than or equal to 1.31 MPa·m^(0.5), from greater thanor equal to 0.79 MPa·m^(0.5) to less than or equal to 1.30 MPa·m^(0.5),from greater than or equal to 0.80 MPa·m^(0.5) to less than or equal to1.29, from greater than or equal to 0.81 MPa·m^(0.5) to less than orequal to 1.28 MPa·m^(0.5), from greater than or equal to 0.82MPa·m^(0.5) to less than or equal to 1.27 MPa·m^(0.5), from greater thanor equal to 0.83 MPa·m^(0.5) to less than or equal to 1.26 MPa·m^(0.5),from greater than or equal to 0.84 MPa·m^(0.5) to less than or equal to1.25 MPa·m^(0.5), from greater than or equal to 0.85 MPa·m^(0.5) to lessthan or equal to 1.24 MPa·m^(0.5), from greater than or equal to 0.86MPa·m^(0.5) to less than or equal to 1.23 MPa·m^(0.5), from greater thanor equal to 0.87 MPa·m^(0.5) to less than or equal to 1.22 MPa·m^(0.5),from greater than or equal to 0.88 MPa·m^(0.5) to less than or equal to1.21 MPa·m^(0.5), from greater than or equal to 0.89 MPa·m^(0.5) to lessthan or equal to 1.20 MPa·m^(0.5), from greater than or equal to 0.90MPa·m^(0.5) to less than or equal to 1.19 MPa·m^(0.5), from greater thanor equal to 0.91 MPa·m^(0.5) to less than or equal to 1.18 MPa·m^(0.5),from greater than or equal to 0.92 MPa·m^(0.5) to less than or equal to1.17 MPa·m^(0.5), from greater than or equal to 0.93 MPa·m^(0.5) to lessthan or equal to 1.16 MPa·m^(0.5), from greater than or equal to 0.94MPa·m^(0.5) to less than or equal to 1.15 MPa·m^(0.5), from greater thanor equal to 0.95 MPa·m^(0.5) to less than or equal to 1.14 MPa·m^(0.5),from greater than or equal to 0.96 MPa·m^(0.5) to less than or equal to1.13 MPa·m^(0.5), from greater than or equal to 0.97 MPa·m^(0.5) to lessthan or equal to 1.12 MPa·m^(0.5), from greater than or equal to 0.98MPa·m^(0.5) to less than or equal to 1.11 MPa·m^(0.5), from greater thanor equal to 0.99 MPa·m^(0.5) to less than or equal to 1.10 MPa·m^(0.5),from greater than or equal to 1.00 MPa·m^(0.5) to less than or equal to1.09 MPa·m^(0.5), from greater than or equal to 1.01 MPa·m^(0.5) to lessthan or equal to 1.08 MPa·m^(0.5), from greater than or equal to 1.02MPa·m^(0.5) to less than or equal to 1.07 MPa·m^(0.5), from greater thanor equal to 1.03 MPa·m^(0.5) to less than or equal to 1.06 MPa·m^(0.5),from greater than or equal to 1.04 MPa·m^(0.5) to less than or equal to1.05 MPa·m^(0.5), and all ranges and sub-ranges between the foregoingvalues. In some embodiments, the compositions utilized to form theglass-based articles exhibit a K_(IC) value greater than or equal to0.90 MPa·m^(0.5). In some embodiments, the compositions utilized to formthe glass-based articles exhibit a K_(IC) value less than or equal to1.5 MPa·m^(0.5).

As utilized herein, the K_(IC) fracture toughness is measured by thedouble cantilever beam (DCB) method. The K_(IC) values were measured onglass-based substrates before being ion exchanged to form theglass-based articles. The DCB specimen geometry is shown in FIG. 1 withimportant parameters being the crack length a, applied load P,cross-sectional dimensions w and 2 h, and the thickness of thecrack-guiding groove b. The samples were cut into rectangles of width 2h=1.25 cm and a thickness ranging from, w=0.3 mm to 1 mm, with theoverall length of the sample, which is not a critical dimension, varyingfrom 5 cm to 10 cm. A hole was drilled on both ends with a diamond drillto provide a means of attaching the sample to a sample holder and to theload. A crack “guiding groove” was cut down the length of the sample onboth flat faces using a wafer dicing saw with a diamond blade, leaving a“web” of material, approximately half the total plate thickness(dimension b in FIG. 1), with a height of 180 μm corresponding to theblade thickness. The high precision dimensional tolerances of the dicingsaw allow for minimal sample-to-sample variation. The dicing saw wasalso used to cut an initial crack where a=15 mm. As a consequence ofthis final operation a very thin wedge of material was created near thecrack tip (due to the blade curvature) allowing for easier crackinitiation in the sample. The samples were mounted in a metal sampleholder with a steel wire in the bottom hole of the sample. The sampleswere also supported on the opposite end to keep the samples level underlow loading conditions. A spring in series with a load cell (FUTEK,LSB200) was hooked to the upper hole which was then extended, togradually apply load, using rope and a high precision slide. The crackwas monitored using a microscope having a 5 μm resolution attached to adigital camera and a computer. The applied stress intensity, K_(P), wascalculated using the following equation (III):

$K_{P} = {\left\lbrack \frac{P \cdot a}{\left( {w \cdot b} \right)^{0.5}h^{1.5}} \right\rbrack \left\lbrack {{{3.4}7} + {{2.3}2\frac{h}{a}}} \right\rbrack}$

For each sample, a crack was first initiated at the tip of the web, andthen the starter crack was carefully sub-critically grown until theratio of dimensions a/h was greater than 1.5, which is required forequation (III) to accurately calculate stress intensity. At this pointthe crack length, a, was measured and recorded using a travelingmicroscope with 5 μm resolution. A drop of toluene was then placed intothe crack groove and wicked along the entire length of groove bycapillary forces, pinning the crack from moving until the fracturetoughness is reached. The load was then increased until sample fractureoccurred, and the critical stress intensity K_(IC) calculated from thefailure load and sample dimensions, with K_(P) being equivalent toK_(IC) due to the measurement method.

The Young's modulus (E) of the glass compositions utilized to form theglass-based articles has a negative correlation with the dropperformance of the glass-based articles, as demonstrated by formulas (I)and (II). In embodiments, the compositions utilized to form theglass-based articles exhibit a Young's modulus (E) from greater than orequal to 75 GPa to less than or equal to 120 GPa, such as from greaterthan or equal to 76 GPa to less than or equal to 115 GPa, from greaterthan or equal to 77 GPa to less than or equal to 113 GPa, from greaterthan or equal to 78 GPa to less than or equal to 112 GPa, from greaterthan or equal to 79 GPa to less than or equal to 111 GPa, from greaterthan or equal to 80 GPa to less than or equal to 110 GPa, from greaterthan or equal to 81 GPa to less than or equal to 109 GPa, from greaterthan or equal to 82 GPa to less than or equal to 108 GPa, from greaterthan or equal to 83 GPa to less than or equal to 107 GPa, from greaterthan or equal to 84 GPa to less than or equal to 106 GPa, from greaterthan or equal to 85 GPa to less than or equal to 105 GPa, from greaterthan or equal to 86 GPa to less than or equal to 104 GPa, from greaterthan or equal to 87 GPa to less than or equal to 103 GPa, from greaterthan or equal to 88 GPa to less than or equal to 102 GPa, from greaterthan or equal to 89 GPa to less than or equal to 101 GPa, from greaterthan or equal to 90 GPa to less than or equal to 100 GPa, from greaterthan or equal to 91 GPa to less than or equal to 99 GPa, from greaterthan or equal to 92 GPa to less than or equal to 98 GPa, from greaterthan or equal to 93 GPa to less than or equal to 97 GPa, from greaterthan or equal to 94 GPa to less than or equal to 96 GPa, or equal to 95GPa, and all ranges and sub-ranges between the foregoing values. Inembodiments, the compositions utilized to form the glass-based articlesexhibit a Young's modulus (E) from greater than or equal to 80 GPa toless than or equal to 120 GPa. The Young's modulus values recited inthis disclosure refer to a value as measured by a resonant ultrasonicspectroscopy technique of the general type set forth in ASTM E2001-13,titled “Standard Guide for Resonant Ultrasound Spectroscopy for DefectDetection in Both Metallic and Non-metallic Parts.”

The hardness (H) of the glass compositions utilized to form theglass-based articles has a positive correlation with the dropperformance of the glass-based articles, as demonstrated by formulas (I)and (II). In embodiments, the compositions utilized to form theglass-based articles exhibit a hardness (H) from greater than or equalto 6.0 GPa to less than or equal to 8.0 GPa, such as from greater thanor equal to 6.1 GPa to less than or equal to 7.9 GPa, from greater thanor equal to 6.2 GPa to less than or equal to 7.8 GPa, from greater thanor equal to 6.3 GPa to less than or equal to 7.7 GPa, from greater thanor equal to 6.4 GPa to less than or equal to 7.6 GPa, from greater thanor equal to 6.5 GPa to less than or equal to 7.5 GPa, from greater thanor equal to 6.6 GPa to less than or equal to 7.4 GPa, from greater thanor equal to 6.7 GPa to less than or equal to 7.3 GPa, from greater thanor equal to 6.8 GPa to less than or equal to 7.2 GPa, from greater thanor equal to 6.9 GPa to less than or equal to 7.1 GPa, or equal to 7.0GPa, and all ranges and sub-ranges between the foregoing values. Thehardness values recited in this disclosure refer to a value as measuredby Vickers hardness test. The Vickers hardness test included indentationwith a Vickers indenter tip for 15 seconds with a 200 gram load.

The glass-based articles may have any suitable thickness. The thickness(t) of the glass-based articles has a negative correlation with the dropperformance of the glass-based articles, as demonstrated by formula (I).In embodiments, the glass-based articles may have a thickness (t) fromgreater than or equal to 0.2 mm to less than or equal to 2.0 mm, such asfrom greater than or equal to 0.3 mm to less than or equal to 1.0 mm,from greater than or equal to 0.4 mm to less than or equal to 0.9 mm,from greater than or equal to 0.5 mm to less than or equal to 0.8 mm,from greater than or equal to 0.6 mm to less than or equal to 0.7 mm,and all ranges and sub-ranges between the foregoing values.

As mentioned above, glass-based articles are strengthened, such as byion exchange, making a glass that is damage resistant for applicationssuch as, but not limited to, articles for display covers or electronicdevice housings. With reference to FIG. 2, the glass-based article has afirst region under compressive stress (e.g., first and secondcompressive layers 120, 122 in FIG. 2) extending from the surface to adepth of compression (DOC) of the glass-based article and a secondregion (e.g., central region 130 in FIG. 2) under a tensile stress orcentral tension (CT) extending from the DOC into the central or interiorregion of the glass-based article. As used herein, DOC refers to thedepth at which the stress within the glass-based article changes fromcompressive to tensile. At the DOC, the stress crosses from a positive(compressive) stress to a negative (tensile) stress and thus exhibits astress value of zero.

According to the convention normally used in the art, compression orcompressive stress is expressed as a negative (<0) stress and tension ortensile stress is expressed as a positive (>0) stress. Throughout thisdescription, however, CS is expressed as a positive or absolutevalue—i.e., as recited herein, CS=|CS|. The compressive stress (CS) hasa maximum at or near the surface of the glass-based article, and the CSvaries with distance d from the surface according to a function.Referring again to FIG. 2, a first segment 120 extends from firstsurface 110 to a depth d₁ and a second segment 122 extends from secondsurface 112 to a depth d₂. Together, these segments define a compressionor CS of glass-based article 100. Compressive stress (including surfaceCS) is measured by surface stress meter (FSM) using commerciallyavailable instruments such as the FSM-6000, manufactured by OriharaIndustrial Co., Ltd. (Japan). Surface stress measurements rely upon theaccurate measurement of the stress optical coefficient (SOC), which isrelated to the birefringence of the glass. SOC in turn is measuredaccording to Procedure C (Glass Disc Method) described in ASTM standardC770-16, entitled “Standard Test Method for Measurement of GlassStress-Optical Coefficient,” the contents of which are incorporatedherein by reference in their entirety.

In some embodiments, the CS of the glass-based article is from greaterthan or equal to 300 MPa to less than or equal to 1300 MPa, such as fromgreater than or equal to 325 MPa to less than or equal to 1250 MPa, fromgreater than or equal to 350 MPa to less than or equal to 1200 MPa, fromgreater than or equal to 375 MPa to less than or equal to 1150 MPa, fromgreater than or equal to 400 MPa to less than or equal to 1100 MPa, fromgreater than or equal to 425 MPa to less than or equal to 1050 MPa, fromgreater than or equal to 450 MPa to less than or equal to 1000 MPa, fromgreater than or equal to 475 MPa to less than or equal to 975 MPa, fromgreater than or equal to 500 MPa to less than or equal to 950 MPa, fromgreater than or equal to 525 MPa to less than or equal to 925 MPa, fromgreater than or equal to 550 MPa to less than or equal to 900 MPa, fromgreater than or equal to 575 MPa to less than or equal to 875 MPa, fromgreater than or equal to 600 MPa to less than or equal to 850 MPa, fromgreater than or equal to 625 MPa to less than or equal to 825 MPa, fromgreater than or equal to 650 MPa to less than or equal to 800 MPa, fromgreater than or equal to 675 MPa to less than or equal to 775 MPa, orfrom greater than or equal to 700 MPa to less than or equal to 750 MPa,and all ranges and sub-ranges between the foregoing values. In someembodiments, the CS of the glass-based article is greater than or equalto 100 MPa.

In one or more embodiments, Na⁺ and K⁺ ions are exchanged into theglass-based article and the Na⁺ ions diffuse to a deeper depth into theglass article than the K⁺ ions. The depth of penetration of K⁺ ions(“Potassium DOL”) is distinguished from DOC because it represents thedepth of potassium penetration as a result of an ion exchange process.The Potassium DOL is typically less than the DOC for the articlesdescribed herein. Potassium DOL is measured using a surface stress metersuch as the commercially available FSM-6000 surface stress meter,manufactured by Orihara Industrial Co., Ltd. (Japan), which relies onaccurate measurement of the stress optical coefficient (SOC), asdescribed above with reference to the CS measurement. The Potassium DOLof each of first and second compressive layers 120, 122 is from greaterthan or equal to 5 μm to less than or equal to 30 μm, such as fromgreater than or equal to 6 μm to less than or equal to 25 μm, fromgreater than or equal to 7 μm to less than or equal to 20 μm, fromgreater than or equal to 8 μm to less than or equal to 15 μm, or fromgreater than or equal to 9 μm to less than or equal to 10 μm, and allranges and sub-ranges between the foregoing values. In otherembodiments, the potassium DOL of each of the first and secondcompressive layers 120, 122 is from greater than or equal to 6 μm toless than or equal to 30 μm, such as from greater than or equal to 10 μmto less than or equal to 30 μm, from greater than or equal to 15 μm toless than or equal to 30 μm, from greater than or equal to 20 μm to lessthan or equal to 30 μm, or from greater than or equal to 25 μm to lessthan or equal to 30 μm, and all ranges and sub-ranges between theforegoing values. In yet other embodiments, the potassium DOL of each ofthe first and second compressive layers 120, 122 is from greater than orequal to 5 μm to less than or equal to 25 μm, such as from greater thanor equal to 5 μm to less than or equal to 20 μm, from greater than orequal to 5 μm to less than or equal to 15 μm, or from greater than orequal to 5 μm to less than or equal to 10 μm, and all ranges andsub-ranges between the foregoing values.

The compressive stress of both major surfaces (110, 112 in FIG. 1) isbalanced by stored tension in the central region (130) of the glass. Themaximum central tension (CT) and DOC values are measured using ascattered light polariscope (SCALP) technique known in the art. TheRefracted near-field (RNF) method or SCALP may be used to measure thestress profile. When the RNF method is utilized to measure the stressprofile, the maximum CT value provided by SCALP is utilized in the RNFmethod. In particular, the stress profile measured by RNF is forcebalanced and calibrated to the maximum CT value provided by a SCALPmeasurement. The RNF method is described in U.S. Pat. No. 8,854,623,entitled “Systems and methods for measuring a profile characteristic ofa glass sample”, which is incorporated herein by reference in itsentirety. The RNF method includes placing the glass article adjacent toa reference block, generating a polarization-switched light beam that isswitched between orthogonal polarizations at a rate of between 1 Hz and50 Hz, measuring an amount of power in the polarization-switched lightbeam and generating a polarization-switched reference signal, whereinthe measured amounts of power in each of the orthogonal polarizationsare within 50% of each other. The method further includes transmittingthe polarization-switched light beam through the glass sample andreference block for different depths into the glass sample, thenrelaying the transmitted polarization-switched light beam to a signalphotodetector using a relay optical system, with the signalphotodetector generating a polarization-switched detector signal. Themethod also includes dividing the detector signal by the referencesignal to form a normalized detector signal and determining the profilecharacteristic of the glass sample from the normalized detector signal.

In embodiments, the glass-based article may have a maximum CT greaterthan or equal to 95 MPa, such as greater than or equal to 100 MPa,greater than or equal to 105 MPa, greater than or equal to 110 MPa,greater than or equal to 110 MPa, greater than or equal to 120 MPa,greater than or equal to 130 MPa, greater than or equal to 140 MPa, orgreater than or equal to 150 MPa, or more. In some embodiments, theglass-based article may have a maximum CT less than or equal to 200 MPa,such as less than or equal to 190 MPa, less than or equal to 180 MPa,less than or equal to 170 MPa, less than or equal to 160 MPa, less thanor equal to 150 MPa, less than or equal to 140 MPa, less than or equalto 130 MPa, less than or equal to 120 MPa, less than or equal to 110MPa, or less than or equal to 100 MPa. It should be understood that, inembodiments, any of the above ranges may be combined with any otherrange. However, in other embodiments, the glass article may have amaximum CT from greater than or equal to 95 MPa to less than or equal to200 MPa, such as from greater than or equal to 100 MPa to less than orequal to 190 MPa, from greater than or equal to 110 MPa to less than orequal to 180 MPa, from greater than or equal to 120 MPa to less than orequal to 170 MPa, from greater than or equal to 130 MPa to less than orequal to 160 MPa, or from greater than or equal to 140 MPa to less thanor equal to 150 MPa, and all ranges and sub-ranges between the foregoingvalues.

The maximum central tension (CT) may also be described with reference tothe thickness of the glass-based article. In embodiments, theglass-based article may have a maximum CT less than or equal to 120/√(t)MPa where t is in mm, such as less than or equal to 110/√(t) MPa, lessthan or equal to 110/√(t) MPa, less than or equal to 100/√(t) MPa, lessthan or equal to 90/√(t) MPa, less than or equal to 80/√(t) MPa, lessthan or equal to 70/√(t) MPa, less than or equal to 60/√(t) MPa, lessthan or equal to 50/√(t) MPa, less than or equal to 40/√(t) MPa, lessthan or equal to 30/√(t) MPa, less than or equal to 20/√(t) MPa, lessthan or equal to 10/√(t) MPa, or less. In embodiments, the glass-basedarticle may have a maximum CT less than or equal to 120/√(t) MPa where tis in mm, such as less than or equal to 110/√(t) MPa, less than or equalto 110/√(t) MPa, less than or equal to 100/√(t) MPa, less than or equalto 90/√(t) MPa, less than or equal to 80/√(t) MPa, less than or equal to70/√(t) MPa, less than or equal to 60/√(t) MPa, less than or equal to50/√(t) MPa, less than or equal to 40/√(t) MPa, less than or equal to30/√(t) MPa, less than or equal to 20/√(t) MPa, less than or equal to10/√(t) MPa, or less. In embodiments, the glass-based article may have amaximum CT greater than or equal to 10/√(t) MPa where t is in mm, suchas greater than or equal to 20/√(t) MPa, greater than or equal to30/√(t) MPa, greater than or equal to 40/√(t) MPa, greater than or equalto 50/√(t) MPa, greater than or equal to 60/√(t) MPa, greater than orequal to 70/√(t) MPa, greater than or equal to 80/√(t) MPa, greater thanor equal to 90/√(t) MPa, greater than or equal to 100/√(t) MPa, greaterthan or equal to 110/√(t) MPa, or more. In embodiments, the glass-basedarticle may have a maximum CT from greater than or equal to 10/√(t) MPato less than or equal to 120/√(t) MPa where t is in mm, such as fromgreater than or equal to 20/√(t) MPa to less than or equal to 110/√(t)MPa, from greater than or equal to 30/√(t) MPa to less than or equal to100/√(t) MPa, from greater than or equal to 40/√(t) MPa to less than orequal to 90/√(t) MPa, from greater than or equal to 50/√(t) MPa to lessthan or equal to 80/√(t) MPa, from greater than or equal to 60/√(t) MPato less than or equal to 70/√(t) MPa, and all ranges and sub-rangesbetween the foregoing values.

The glass-based articles may have any appropriate depth of compression(DOC). In embodiments, the DOC is from greater than or equal to 75 μm toless than or equal to 300 μm, such as from greater than or equal to 85μm to less than or equal to 290 μm, from greater than or equal to 95 μmto less than or equal to 280 μm, from greater than or equal to 100 μm toless than or equal to 270 μm, from greater than or equal to 110 μm toless than or equal to 260 μm, from greater than or equal to 120 μm toless than or equal to 250 μm, from greater than or equal to 130 μm toless than or equal to 240 μm, from greater than or equal to 140 μm toless than or equal to 230 μm, from greater than or equal to 150 μm toless than or equal to 220 μm, from greater than or equal to 160 μm toless than or equal to 210 μm, from greater than or equal to 170 μm toless than or equal to 200 μm, from greater than or equal to 180 am toless than or equal to 190 μm, and all ranges and sub-ranges between theforegoing values.

The DOC is provided in some embodiments herein as a portion of thethickness (t) of the glass-based article. In embodiments, the glassarticles may have a depth of compression (DOC) from greater than orequal to 0.15t to less than or equal to 0.40t, such as from greater thanor equal to 0.18t to less than or equal to 0.38t, or from greater thanor equal to 0.19t to less than or equal to 0.36t, from greater than orequal to 0.20t to less than or equal to 0.34t, from greater than orequal to 0.18t to less than or equal to 0.32t, from greater than orequal to 0.19t to less than or equal to 0.30t, from greater than orequal to 0.20t to less than or equal to 0.29t, from greater than orequal to 0.21t to less than or equal to 0.28t, from greater than orequal to 0.22t to less than or equal to 0.27t, from greater than orequal to 0.23t to less than or equal to 0.26t, or from greater than orequal to 0.24t to less than or equal to 0.25t, and all ranges andsub-ranges between the foregoing values.

The glass-based articles described herein may exhibit a stored tensileenergy (STE) in any appropriate amount. In embodiments, the glass-basedarticles may have a STE greater than or equal to 5 Pa·m, such as greaterthan or equal to 6 Pa·m, greater than or equal to 7 Pa·m, greater thanor equal to 8 Pa·m, greater than or equal to 9 Pa·m, greater than orequal to 10 Pa·m, greater than or equal to 11 Pa·m, greater than orequal to 12 Pa·m, greater than or equal to 13 Pa·m, greater than orequal to 14 Pa·m, greater than or equal to 15 Pa·m, greater than orequal to 16 Pa·m, greater than or equal to 17 Pa·m, greater than orequal to 18 Pa·m, greater than or equal to 19 Pa·m, greater than orequal to 20 Pa·m, greater than or equal to 21 Pa·m, greater than orequal to 22 Pa·m, greater than or equal to 23 Pa·m, greater than orequal to 24 Pa·m, greater than or equal to 25 Pa·m, greater than orequal to 26 Pa·m, greater than or equal to 27 Pa·m, greater than orequal to 28 Pa·m, greater than or equal to 29 Pa·m, or more. Inembodiments, the glass-based articles may have a STE less than or equalto 30 Pa·m, such as less than or equal to 29 Pa·m, less than or equal to28 Pa·m, less than or equal to 27 Pa·m, less than or equal to 26 Pa·m,less than or equal to 25 Pa·m, less than or equal to 24 Pa·m, less thanor equal to 23 Pa·m, less than or equal to 22 Pa·m, less than or equalto 21 Pa·m, less than or equal to 20 Pa·m, less than or equal to 19Pa·m, less than or equal to 18 Pa·m, less than or equal to 17 Pa·m, lessthan or equal to 16 Pa·m, less than or equal to 15 Pa·m, less than orequal to 14 Pa·m, less than or equal to 13 Pa·m, less than or equal to12 Pa·m, less than or equal to 11 Pa·m, less than or equal to 10 Pa·m,less than or equal to 9 Pa·m, less than or equal to 8 Pa·m, less than orequal to 7 Pa·m, less than or equal to 6 Pa·m, less than or equal to 5Pa·m, or less. In embodiments, the glass-based articles may have a STEfrom greater than or equal to 5 Pa·m to less than or equal to 30 Pa·m,such as greater than or equal to 6 Pa·m to less than or equal to 29Pa·m, greater than or equal to 7 Pa·m to less than or equal to 28 Pa·m,greater than or equal to 8 Pa·m to less than or equal to 27 Pa·m,greater than or equal to 8 Pa·m to less than or equal to 26 Pa·m,greater than or equal to 9 Pa·m to less than or equal to 25 Pa·m,greater than or equal to 10 Pa·m to less than or equal to 24 Pa·m,greater than or equal to 11 Pa·m to less than or equal to 23 Pa·m,greater than or equal to 12 Pa·m to less than or equal to 23 Pa·m,greater than or equal to 13 Pa·m to less than or equal to 22 Pa·m,greater than or equal to 14 Pa·m to less than or equal to 21 Pa·m,greater than or equal to 15 Pa·m to less than or equal to 20 Pa·m,greater than or equal to 16 Pa·m to less than or equal to 19 Pa·m,greater than or equal to 17 Pa·m to less than or equal to 18 Pa·m, andall ranges and sub-ranges between the foregoing values.

As utilized herein, the stored tensile energy (STE) of the glass-basedarticles is calculated using the following equation (IV):

STE(Pa·m)=[1−v]/E∫σ(z){circumflex over ( )}2dz

where v is Poisson's ratio, E is the Young's modulus, σ(z) is the stressas a function of position (z) in the thickness direction, and theintegration is performed over the tensile region only. Equation (IV) isdescribed in Suresh T. Gulati, Frangibility of Tempered Soda-Lime GlassSheet, GLASS PROCESSING DAYS, The Fifth International Conference onArchitectural and Automotive Glass, 13-15 Sep. 1997, as equation number4. The Poisson's ratio values recited in this disclosure refer to avalue as measured by a resonant ultrasonic spectroscopy technique of thegeneral type set forth in ASTM E2001-13, titled “Standard Guide forResonant Ultrasound Spectroscopy for Defect Detection in Both Metallicand Non-metallic Parts.”

The glass-based articles may be formed by exposing glass-basedsubstrates to an ion exchange solution to form a glass-based articlehaving a compressive stress layer extending from a surface of theglass-based article to a depth of compression. The ion exchange processmay be conducted under conditions sufficient to produce a glass-basedarticle satisfying any of formulas (I), (IA), and (II). In embodiments,the ion exchange solution may be molten nitrate salt. In someembodiments, the ion exchange solution may be molten KNO₃, molten NaNO₃,or combinations thereof. In certain embodiments, the ion exchangesolution may comprise less than about 95% molten KNO₃, such as less thanabout 90% molten KNO₃, less than about 80% molten KNO₃, less than about70% molten KNO₃, less than about 60% molten KNO₃, or less than about 50%molten KNO₃. In certain embodiments, the ion exchange solution maycomprise at least about 5% molten NaNO₃, such as at least about 10%molten NaNO₃, at least about 20% molten NaNO₃, at least about 30% moltenNaNO₃, or at least about 40% molten NaNO₃. In other embodiments, the ionexchange solution may comprise about 95% molten KNO₃ and about 5% moltenNaNO₃, about 94% molten KNO₃ and about 6% molten NaNO₃, about 93% moltenKNO₃ and about 7% molten NaNO₃, about 80% molten KNO₃ and about 20%molten NaNO₃, about 75% molten KNO₃ and about 25% molten NaNO₃, about70% molten KNO₃ and about 30% molten NaNO₃, about 65% molten KNO₃ andabout 35% molten NaNO₃, or about 60% molten KNO₃ and about 40% moltenNaNO₃, and all ranges and sub-ranges between the foregoing values. Inembodiments, other sodium and potassium salts may be used in the ionexchange solution, such as, for example sodium or potassium nitrites,phosphates, or sulfates.

In some embodiments, the ion exchange solution may include lithiumsalts, such as LiNO₃. The glass-based substrate may be exposed to theion exchange solution by dipping the glass-based substrate into a bathof the ion exchange solution, spraying the ion exchange solution ontothe glass-based substrate, or otherwise physically applying the ionexchange solution to the glass-based substrate. Upon exposure to theglass-based substrate, the ion exchange solution may, according toembodiments, be at a temperature from greater than or equal to 340° C.to less than or equal to 500° C., such as from greater than or equal to350° C. to less than or equal to 490° C., from greater than or equal to360° C. to less than or equal to 480° C., from greater than or equal to370° C. to less than or equal to 470° C., from greater than or equal to380° C. to less than or equal to 460° C., from greater than or equal to390° C. to less than or equal to 450° C., from greater than or equal to400° C. to less than or equal to 440° C., from greater than or equal to410° C. to less than or equal to 430° C., equal to 420° C., and allranges and sub-ranges between the foregoing values. In embodiments, theglass composition may be exposed to the ion exchange solution for aduration from greater than or equal to 2 hours to less than or equal to48 hours, such as from greater than or equal to 4 hours to less than orequal to 44 hours, from greater than or equal to 8 hours to less than orequal to 40 hours, from greater than or equal to 12 hours to less thanor equal to 36 hours, from greater than or equal to 16 hours to lessthan or equal to 32 hours, from greater than or equal to 20 hours toless than or equal to 28 hours, equal to 24 hours, and all ranges andsub-ranges between the foregoing values.

The ion exchange process may be performed in an ion exchange solutionunder processing conditions that provide an improved compressive stressprofile as disclosed, for example, in U.S. Patent ApplicationPublication No. 2016/0102011, which is incorporated herein by referencein its entirety. In some embodiments, the ion exchange process may beselected to form a parabolic stress profile in the glass articles, suchas those stress profiles described in U.S. Patent ApplicationPublication No. 2016/0102014, which is incorporated herein by referencein its entirety.

After an ion exchange process is performed, it should be understood thata composition at the surface of the glass-based article is differentthan the composition of the glass-based substrate before it undergoes anion exchange process. This results from one type of alkali metal ion inthe as-formed glass, such as, for example Li⁺ or Na⁺, being replacedwith larger alkali metal ions, such as, for example Na⁺ or K⁺,respectively. However, the glass composition and phase assemblage at ornear the center of the depth of the glass-based article will, inembodiments, still have the composition of the glass-based substrate.

The glass-based substrates that are ion exchanged to form theglass-based articles may have any appropriate composition, such asalkali aluminosilicate compositions. In embodiments, the glass-basedsubstrates include SiO₂, Al₂O₃, B₂O₃, and at least one alkali metaloxide. The at least one alkali metal oxide facilitates the ion exchangeof the glass-based substrates. For example, the glass-based substratemay include Li₂O and/or Na₂O that facilitate the exchange of Na⁺ and K⁺ions into the glass-based substrate to form the glass-based articles. Asdiscussed above, the composition of the glass-based substrates may beequivalent to the composition and phase assemblage at the center of theglass-based article.

In embodiments of glass-based substrates described herein, theconcentration of constituent components (e.g., SiO₂, Al₂O₃, Li₂, and thelike) are given in mole percent (mol %) on an oxide basis, unlessotherwise specified. Components of the glass-based substrate accordingto embodiments are discussed individually below. It should be understoodthat any of the variously recited ranges of one component may beindividually combined with any of the variously recited ranges for anyother component.

In embodiments of the glass-based substrates disclosed herein, SiO₂ isthe largest constituent and, as such, SiO₂ is the primary constituent ofthe glass network formed from the glass composition. Pure SiO₂ has arelatively low CTE and is alkali free. However, pure SiO₂ has a highmelting point. Accordingly, if the concentration of SiO₂ in theglass-based substrate is too high, the formability of the glasscomposition may be diminished as higher concentrations of SiO₂ increasethe difficulty of melting the glass, which, in turn, adversely impactsthe formability of the glass. In embodiments, the glass-based substrategenerally comprises SiO₂ in an amount from greater than or equal to 50.0mol % to less than or equal to 69.0 mol %, and all ranges and sub-rangesbetween the foregoing values. In embodiments, the glass-based substratecomprises SiO₂ in an amount from greater than or equal to 51.0 mol % toless than or equal to 68.0 mol %, such as from greater than or equal to52.0 mol % to less than or equal to 67.0 mol %, from greater than orequal to 53.0 mol % to less than or equal to 66.0 mol %, from greaterthan or equal to 54.0 mol % to less than or equal to 65.0 mol %, fromgreater than or equal to 55.0 mol % to less than or equal to 64.0 mol %,from greater than or equal to 56.0 mol % to less than or equal to 63.0mol %, from greater than or equal to 57.0 mol % to less than or equal to62.0 mol %, from greater than or equal to 58.0 mol % to less than orequal to 61.0 mol %, or from greater than or equal to 60.0 mol % to lessthan or equal to 61.0 mol %, and all ranges and sub-ranges between theforegoing values.

The glass-based substrate of embodiments may further comprise Al₂O₃.Al₂O₃ may serve as a glass network former, similar to SiO₂. Al₂O₃ mayincrease the viscosity of the glass composition due to its tetrahedralcoordination in a glass melt formed from a glass composition, decreasingthe formability of the glass composition when the amount of Al₂O₃ is toohigh. However, when the concentration of Al₂O₃ is balanced against theconcentration of SiO₂ and the concentration of alkali oxides in theglass-based substrate, Al₂O₃ can reduce the liquidus temperature of theglass melt, thereby enhancing the liquidus viscosity and improving thecompatibility of the glass composition with certain forming processes,such as the fusion forming process. In embodiments, the glass-basedsubstrate generally comprises Al₂O₃ in a concentration of from greaterthan or equal to 12.5 mol % to less than or equal to 25.0 mol %, and allranges and sub-ranges between the foregoing values. In embodiments, theglass-based substrate comprises Al₂O₃ in an amount from greater than orequal to 13.0 mol % to less than or equal to 24.5 mol %, such as fromgreater than or equal to 13.5 mol % to less than or equal to 24.0 mol %,from greater than or equal to 14.0 mol % to less than or equal to 23.5mol %, from greater than or equal to 14.5 mol % to less than or equal to23.0 mol %, from greater than or equal to 15.0 mol % to less than orequal to 22.5 mol %, from greater than or equal to 15.5 mol % to lessthan or equal to 22.0 mol %, from greater than or equal to 16.0 mol % toless than or equal to 21.5 mol %, from greater than or equal to 16.5 mol% to less than or equal to 21.0 mol %, from greater than or equal to17.0 mol % to less than or equal to 20.5 mol %, from greater than orequal to 17.5 mol % to less than or equal to 20.0 mol %, from greaterthan or equal to 18.0 mol % to less than or equal to 19.5 mol %, or fromgreater than or equal to 18.5 mol % to less than or equal to 19.0 mol %,and all ranges and sub-ranges between the foregoing values.

Like SiO₂ and Al₂O₃, B₂O₃ may be added to the glass-based substrate as anetwork former, thereby reducing the meltability and formability of theglass composition. Thus, B₂O₃ may be added in amounts that do not overlydecrease these properties. In embodiments, the glass-based substrate maycomprise B₂O₃ in amounts from greater than or equal to 0 mol % B₂O₃ toless than or equal to 8.0 mol % B₂O₃, and all ranges and sub-rangesbetween the foregoing values. In embodiments, the glass-based substratecomprises B₂O₃ in amounts from greater than or equal to 0.5 mol % toless than or equal to 7.5 mol %, such as greater than or equal to 1.0mol % to less than or equal to 7.0 mol %, greater than or equal to 1.5mol % to less than or equal to 6.5 mol %, greater than or equal to 2.0mol % to less than or equal to 6.0 mol %, greater than or equal to 2.5mol % to less than or equal to 5.5 mol %, greater than or equal to 3.0mol % to less than or equal to 5.0 mol %, or greater than or equal to3.5 mol % to less than or equal to 4.5 mol %, and all ranges andsub-ranges between the foregoing values.

The inclusion of Li₂O in the glass-based substrate allows for bettercontrol of an ion exchange process and further reduces the softeningpoint of the glass, thereby increasing the manufacturability of theglass. In embodiments, the glass-based substrate generally comprisesLi₂O in an amount from greater than 8.0 mol % to less than or equal to18.0 mol %, and all ranges and sub-ranges between the foregoing values.In embodiments, the glass-based substrate comprises Li₂ in an amountfrom greater than or equal to 8.5 mol % to less than or equal to 17.5mol %, such as from greater than or equal to 9.0 mol % to less than orequal to 17.0 mol %, from greater than or equal to 9.5 mol % to lessthan or equal to 16.5 mol %, from greater than or equal to 10.0 mol % toless than or equal to 16.0 mol %, from greater than or equal to 10.5 mol% to less than or equal to 15.5 mol %, from greater than or equal to11.0 mol % to less than or equal to 15.0 mol %, from greater than orequal to 11.5 mol % to less than or equal to 14.5 mol %, from greaterthan or equal to 12.0 mol % to less than or equal to 14.0 mol %, or fromgreater than or equal to 12.5 mol % to less than or equal to 13.5 mol %,and all ranges and sub-ranges between the foregoing values.

According to embodiments, the glass-based substrate may also comprisealkali metal oxides other than Li₂O, such as Na₂O. Na₂O aids in the ionexchangeability of the glass composition, and also improves theformability, and thereby manufacturability, of the glass composition.However, if too much Na₂O is added to the glass-based substrate, the CTEmay be too low, and the melting point may be too high. In embodiments,the glass-based substrate generally comprises Na₂O in an amount fromgreater than or equal to 0.5 mol % Na₂O to less than or equal to 8.0 mol% Na₂O, and all ranges and sub-ranges between the foregoing values. Inembodiments, the glass-based substrate comprises Na₂O in an amount fromgreater than or equal to 1.0 mol % to less than or equal to 7.5 mol %,such as from greater than or equal to 1.5 mol % to less than or equal to7.0 mol %, from greater than or equal to 2.0 mol % to less than or equalto 6.5 mol %, from greater than or equal to 2.5 mol % to less than orequal to 6.0 mol %, from greater than or equal to 3.0 mol % to less thanor equal to 5.5 mol %, from greater than or equal to 3.5 mol % to lessthan or equal to 5.0 mol %, or from greater than or equal to 4.0 mol %to less than or equal to 4.5 mol %, and all ranges and sub-rangesbetween the foregoing values.

Like Na₂, K₂O also promotes ion exchange and increases the DOC of acompressive stress layer. However, adding K₂O may cause the CTE may betoo low, and the melting point may be too high. In some embodiment, theglass-based substrate can include K₂O. In embodiments, the glasscomposition is substantially free of potassium. As used herein, the term“substantially free” means that the component is not added as acomponent of the batch material even though the component may be presentin the final glass in very small amounts as a contaminant, such as lessthan 0.01 mol %. In other embodiments, K₂O may be present in theglass-based substrate in amounts less than 1 mol %.

MgO lowers the viscosity of a glass, which enhances the formability andmanufacturability of the glass. The inclusion of MgO in the glass-basedsubstrate also improves the strain point and the Young's modulus of theglass composition, and may also improve the ion exchange ability of theglass. However, when too much MgO is added to the glass composition, thedensity and the CTE of the glass composition increase undesirably. Inembodiments, the glass-based substrate generally comprises MgO in aconcentration of from greater than 0 mol % to less than or equal to 17.5mol %, and all ranges and sub-ranges between the foregoing values. Inembodiments, the glass-based substrate comprises MgO in an amount fromgreater than or equal to 0.5 mol % to less than or equal to 17.0 mol %,such as from greater than or equal to 1.0 mol % to less than or equal to16.5 mol %, from greater than or equal to 1.5 mol % to less than orequal to 16.0 mol %, from greater than or equal to 2.0 mol % to lessthan or equal to 15.5 mol %, from greater than or equal to 2.5 mol % toless than or equal to 15.0 mol %, from greater than or equal to 3.0 mol% to less than or equal to 14.5 mol %, from greater than or equal to 3.5mol % to less than or equal to 14.0 mol %, from greater than or equal to4.0 mol % to less than or equal to 13.5 mol %, from greater than orequal to 4.5 mol % to less than or equal to 13.0 mol %, from greaterthan or equal to 5.0 mol % to less than or equal to 12.5 mol %, fromgreater than or equal to 5.5 mol % to less than or equal to 12.0 mol %,from greater than or equal to 6.0 mol % to less than or equal to 11.5mol %, from greater than or equal to 6.5 mol % to less than or equal to11.0 mol %, from greater than or equal to 7.0 mol % to less than orequal to 10.5 mol %, from greater than or equal to 7.5 mol % to lessthan or equal to 10.0 mol %, from greater than or equal to 8.0 mol % toless than or equal to 9.5 mol %, or from greater than or equal to 8.5mol % to less than or equal to 9.0 mol %, and all ranges and sub-rangesbetween the foregoing values.

CaO lowers the viscosity of a glass, which enhances the formability, thestrain point and the Young's modulus, and may improve the ion exchangeability. However, when too much CaO is added to the glass-basedsubstrate, the density and the CTE of the glass composition increase. Inembodiments, the glass-based substrate generally comprises CaO in aconcentration of from greater than 0 mol % to less than or equal to 4.0mol %, and all ranges and sub-ranges between the foregoing values. Inembodiments, the glass-based substrate comprises CaO in an amount fromgreater than or equal to 0.5 mol % to less than or equal to 3.5 mol %,such as from greater than or equal to 1.0 mol % to less than or equal to3.0 mol %, or from greater than or equal to 1.5 mol % to less than orequal to 2.5 mol %, and all ranges and sub-ranges between the foregoingvalues.

La₂O₃ increases the toughness of the glass, and also increases theYoung's modulus and hardness of the glass. However, when too much La₂O₃is added to the glass composition, the glass becomes susceptible todevitrification and the manufacturability of the glass is decreased. Inembodiments, the glass-based substrate generally comprises La₂O₃ in aconcentration of from greater than or equal to 0 mol % to less than orequal to 2.5 mol %, and all ranges and sub-ranges between the foregoingvalues. In embodiments, the glass-based substrate comprises La₂O₃ in anamount from greater than or equal to 0.5 mol % to less than or equal to2.0 mol %, such as from greater than or equal to 1.0 mol % to less thanor equal to 1.5 mol %, and all ranges and sub-ranges between theforegoing values. In some embodiments, the glass composition is free orsubstantially free of La₂O₃.

Y₂O₃ also increases the toughness of the glass, and increases theYoung's modulus and hardness of the glass. However, when too much Y₂O₃is added to the glass composition, the glass becomes susceptible todevitrification and the manufacturability of the glass is decreased. Inembodiments, the glass-based substrate comprises Y₂O₃, such as in aconcentration of from greater than or equal to 0 mol % to less than orequal to 2.0 mol %, and all ranges and sub-ranges between the foregoingvalues. In embodiments, the glass-based substrate comprises Y₂O₃ in anamount from greater than or equal to 0.5 mol % to less than or equal to1.5 mol %. In some embodiments, the glass-based substrate is free orsubstantially free of Y₂O₃.

TiO₂ also contributes to the increased toughness of the glass, whilealso simultaneously softening the glass. However, when too much TiO₂ isadded to the glass composition, the glass becomes susceptible todevitrification and exhibits an undesirable coloration. In embodiments,the glass-based substrate comprises TiO₂, such as in a concentration offrom greater than or equal to 0 mol % to less than or equal to 2.0 mol%, and all ranges and sub-ranges between the foregoing values. Inembodiments, the glass-based substrate comprises TiO₂ in an amount fromgreater than or equal to 0.5 mol % to less than or equal to 1.5 mol %.In some embodiments, the glass-based substrate is free or substantiallyfree of TiO₂.

ZrO₂ contributes to the toughness of the glass. However, when too muchZrO₂ is added to the glass composition, undesirable zirconia inclusionsmay be formed in the glass due at least in part to the low solubility ofZrO₂ in the glass. In embodiments, the glass-based substrate comprisesZrO₂, such as in a concentration of from greater than or equal to 0 mol% to less than or equal to 2.5 mol %, and all ranges and sub-rangesbetween the foregoing values. In embodiments, the glass-based substratecomprises ZrO₂ in an amount from greater than or equal to 0.5 mol % toless than or equal to 2.0 mol %, such as from greater than or equal to1.0 mol % to less than or equal to 1.5 mol %, and all ranges andsub-ranges between the foregoing values. In some embodiments, theglass-based substrate is free or substantially free of ZrO₂.

SrO lowers the liquidus temperature of glass compositions disclosedherein. In embodiments, the glass-based substrate may comprise SrO inamounts from greater than or equal to 0 mol % to less than or equal to1.0 mol %, such as from greater than or equal to 0.2 mol % to less thanor equal to 0.8 mol %, or from greater than or equal to 0.4 mol % toless than or equal to 0.6 mol %, and all ranges and sub-ranges betweenthe foregoing values. In some embodiments, the glass-based substrate maybe substantially free or free of SrO.

In embodiments, the glass-based substrate may optionally include one ormore fining agents. In some embodiments, the fining agents may include,for example, SnO₂. In such embodiments, SnO₂ may be present in theglass-based substrate in an amount less than or equal to 0.2 mol %, suchas from greater than or equal to 0 mol % to less than or equal to 0.1mol %, and all ranges and sub-ranges between the foregoing values. Inother embodiments, SnO₂ may be present in the glass-based substrate inan amount from greater than or equal to 0 mol % to less than or equal to0.2 mol %, or greater than or equal to 0.1 mol % to less than or equalto 0.2 mol %, and all ranges and sub-ranges between the foregoingvalues. In some embodiments, the glass-based substrate may besubstantially free or free of SnO₂.

In embodiments, the glass-based substrate may be substantially free ofone or both of arsenic and antimony. In other embodiments, theglass-based substrate may be free of one or both of arsenic andantimony.

In one or more embodiments, the glass articles described herein mayexhibit an amorphous microstructure and may be substantially free ofcrystals or crystallites. In other words, the glass articles excludeglass-ceramic materials in some embodiments.

The glass-based substrate may include a glass ceramic. The glass ceramicis characterized by a phase assemblage, the phase assemblage includingan amorphous phase and at least one crystalline phase. The crystallinephase(s) of the glass ceramic may include any appropriate crystalstructure, such as a lithium silicate, beta-spodumene, or spinel crystalstructures. The glass ceramic containing glass-based substrates may beformed by any appropriate method, such as ceramming a precursor glass.

The glass-based substrates may be produced by any appropriate method. Inembodiments, the glass-based substrates may be formed by processincluding slot forming, float forming, rolling processes, and fusionforming processes. Drawing processes for forming glass-based substrates,are desirable because they allow a thin glass article to be formed withfew defects.

The glass-based substrates may be characterized by the manner in whichit may be formed. For instance, the glass-based substrate may becharacterized as float-formable (i.e., formed by a float process),down-drawable and, in particular, fusion-formable or slot-drawable(i.e., formed by a down draw process such as a fusion draw process or aslot draw process).

Some embodiments of the glass-based articles described herein may beformed by a down-draw process. Down-draw processes produce glass-basedsubstrates having a uniform thickness that possess relatively pristinesurfaces. Because the average flexural strength of the glass-basedsubstrate and resulting glass-based article is controlled by the amountand size of surface flaws, a pristine surface that has had minimalcontact has a higher initial strength. In addition, down drawnglass-based substrates have a very flat, smooth surface that can be usedin its final application without costly grinding and polishing.

Some embodiments of the glass-based substrates may be described asfusion-formable (i.e., formable using a fusion draw process). The fusionprocess uses a drawing tank that has a channel for accepting moltenglass raw material. The channel has weirs that are open at the top alongthe length of the channel on both sides of the channel. When the channelfills with molten material, the molten glass overflows the weirs. Due togravity, the molten glass flows down the outside surfaces of the drawingtank as two flowing glass films.

These outside surfaces of the drawing tank extend down and inwardly sothat they join at an edge below the drawing tank. The two flowing glassfilms join at this edge to fuse and form a single flowing glass article.The fusion draw method offers the advantage that, because the two glassfilms flowing over the channel fuse together, neither of the outsidesurfaces of the resulting glass-based substrate comes in contact withany part of the apparatus. Thus, the surface properties of the fusiondrawn glass-based substrate are not affected by such contact.

Some embodiments of the glass-based substrates described herein may beformed by a slot draw process. The slot draw process is distinct fromthe fusion draw method. In slot draw processes, the molten raw materialglass is provided to a drawing tank. The bottom of the drawing tank hasan open slot with a nozzle that extends the length of the slot. Themolten glass flows through the slot/nozzle and is drawn downward as acontinuous glass-based substrate and into an annealing region.

The glass-based articles disclosed herein may be incorporated intoanother article such as an article with a display (or display articles)(e.g., consumer electronics, including mobile phones, tablets,computers, navigation systems, and the like), architectural articles,transportation articles (e.g., automobiles, trains, aircraft, sea craft,etc.), appliance articles, or any article that requires sometransparency, scratch-resistance, abrasion resistance or a combinationthereof. An exemplary article incorporating any of the glass-basedarticles disclosed herein is shown in FIGS. 3A and 3B. Specifically,FIGS. 3A and 3B show a consumer electronic device 200 including ahousing 202 having front 204, back 206, and side surfaces 208;electrical components (not shown) that are at least partially inside orentirely within the housing and including at least a controller, amemory, and a display 210 at or adjacent to the front surface of thehousing; and a cover substrate 212 at or over the front surface of thehousing such that it is over the display. The cover substrate 212 and/orthe housing may include any of the glass-based articles disclosedherein.

EXAMPLES

Embodiments will be further clarified by the following examples. Itshould be understood that these examples are not limiting to theembodiments described above.

Glass-based articles with the compositions in Table I below wereprepared, the concentrations of the components are provided in mol %.Example 1 was cerammed to form a glass ceramic. The glass-basedsubstrates had a thickness of 0.8 mm.

TABLE 1 A B C D 1 2 3 SiO₂ 57.43 63.64 63.31 70.94 70.29 54.52 58.09Al₂O₃ 16.10 15.07 15.20 12.83 4.23 19.43 18.04 B₂O₃ 2.34 6.74 1.86 7.916.05 P₂O₅ 6.54 2.53 0.87 Li₂O 5.93 6.82 8.22 21.35 11.70 11.36 Na₂O17.05 9.27 4.30 2.36 1.51 1.90 1.92 ZrO₂ 1.67 CaO 1.55 0.07 0.04 K₂O0.05 MgO 2.81 1.00 2.87 4.35 4.41 SnO₂ 0.07 0.05 0.05 0.06 0.08 0.040.05 TiO₂ ZnO 1.17 0.83 SrO 1.02 Fe₂O₃ 0.02

The glass-based substrates were then ion exchanged to produceglass-based articles. The properties of the glass-based substrates andthe glass-based articles are provided in Table 2 below. The Young'smodulus (E), hardness (H), and fracture toughness (K_(IC)) were measuredon glass-based substrates before being ion exchanged to form theglass-based articles. To measure the drop performance, the glass-basedarticles were loaded into a puck simulating a smart phone and droppedonto 30 grit sandpaper, the drop performance is reported in terms of themaximum drop height in cm before failure of the glass-based article.

TABLE 2 A B C D 1 2 3 K_(IC) 0.65 0.75 0.87 0.84 1.34 0.96 0.95 (MPa√m)E 65 74 77 80 110 (Gpa) H 4.802 5.253 5.733 5.929 7.428 (Gpa) DOC 0.00010.00016 0.00017 0.000175 0.00015 0.00019 0.00019 (m) DOC/t 0.13 0.200.21 0.22 0.19 0.24 0.24 STE 18 12 17 20 8 24 24 (Pa·m) K_(IC) ²*DOC/2.24 × 3.90 × 6.63 × 6.90 × 9.52 × 1.07 × 1.05 × t*√(STE) 10¹¹ 10¹¹ 10¹¹10¹¹ 10¹¹ 10¹² 10¹² (Pa^(2.5)m^(1.5)) K_(IC) ²*DOC*H/ 13242554 2213055439500547 40926356 54876097 E*√(STE) (Pa^(2.5)m^(2.5)) Drop 35 84 135 129182 177 188 Performance (cm)

The relationship between the drop performance and the formula (I) valuesis shown in FIG. 4. The relationship between the drop performance andthe formula (II) values is shown in FIG. 5. As demonstrated by FIGS. 4and 5, glass-based articles satisfying formulas (I) and (II) exhibitimproved drop performance. As demonstrated in FIGS. 4 and 5, Examples1-3 which satisfy formulas (I) and (II) all exhibited better dropperformance than Comparative Examples A-D which did not satisfy formulas(I) and (II).

All ranges disclosed in this specification include any and all rangesand subranges encompassed by the broadly disclosed ranges whether or notexplicitly stated before or after a range is disclosed.

It will be apparent to those skilled in the art that variousmodifications and variations can be made to the embodiments describedherein without departing from the spirit and scope of the claimedsubject matter. Thus it is intended that the specification cover themodifications and variations of the various embodiments described hereinprovided such modification and variations come within the scope of theappended claims and their equivalents.

What is claimed is:
 1. A consumer electronic product, comprising: ahousing having a front surface; a display at or adjacent the frontsurface; and a cover comprising glass disposed over the display, whereinthe glass comprises, in terms of constituents, at least 51.0 mol % SiO₂and no more than 68.0 mol % SiO₂; at least 13.0 mol % Al₂O₃ and no morethan 24.5 mol % Al₂O₃; at least 0.5 mol % B₂O₃ and no more than 7.5 mol% B₂O₃; at least 8.0 mol % Li₂O and no more than 18.0 mol % Li₂O; atleast 0.5 mol % MgO and no more than 17.0 mol % MgO; at least 0.5 mol %CaO and no more than 3.5 mol % CaO; at least 0.5 mol % La₂O₃ and no morethan 2.0 mol % La₂O₃; at least 0.5 mol % Y₂O₃ and no more than 1.5 mol %Y₂O₃; at least 0.5 mol % TiO₂ and no more than 1.5 mol % TiO₂; and atleast 0.5 mol % ZrO₂ and no more than 2.0 mol % ZrO₂; and wherein theglass has a fracture toughness (K_(IC)) of at least 0.75 MPa√{squareroot over (m)}.
 2. A method of measuring fracture toughness of glass,comprising: sub-critically growing a crack in a sample of a glass; aftersub-critically growing the crack, pinning the crack; after pinning thecrack, fracturing the sample by increasing load on the sample untilfailure; and calculating stress intensity K_(IC) of the glass as afunction of the load at failure and dimensions of the sample.
 3. Themethod of claim 2, wherein the pinning comprises wicking an agent intothe crack along a length of the crack.
 4. The method of claim 3, whereinthe agent is toluene.
 5. The method of claim 2, wherein, before thepinning, the crack is sub-critically grown until a ratio of crack lengthto half of a width of the sample is greater than 1.5.
 6. The method ofclaim 2, wherein the sample is rectangular.
 7. The method of claim 6,wherein a first thickness of the sample is between 0.3 mm and 1 mm. 8.The method of claim 7, wherein the sample comprises a web having asecond thickness less than the first thickness.
 9. The method of claim8, wherein the second thickness is approximately half the firstthickness.
 10. The method of claim 9, wherein the dimensions used incalculating the stress intensity K_(IC) include the first and secondthicknesses.
 11. The method of claim 10, wherein the stress intensityK_(IC) is calculated by calculating applied stress intensity K_(P) ofthe glass.
 12. The method of claim 2, wherein the load is applied to thesample by way of a spring attached to a hole in the sample.
 13. Themethod of claim 12, wherein a load cell is in series with the spring.14. The method of claim 13, further comprising monitoring the crack. 15.The method of claim 14, wherein the monitoring includes using amicroscope attached to a digital camera and computer.
 16. The method ofclaim 2, wherein the sample comprises a guiding groove down a length ofthe sample.
 17. The method of claim 16, wherein the sample has two majorsurfaces, and the guiding groove extends down both major surfaces andforms a web.
 18. The method of claim 17, further comprising cutting aninitial crack through the web and within the guiding groove.
 19. Themethod of claim 18, wherein the cutting of the initial crack comprisesusing a dicing saw.
 20. The method of claim 19, wherein the initialcrack includes a wedge formed by curvature of the dicing saw.